Before starting, a definition: Any combination of numbers and letters and arithmetical operations (including = < > <= >=) with more than three symbols is an algebra “thing”. So, in passing, observe that a “number sentence” is an algebra “thing”.

f(x) = 3x + 2 This means “The rule for the function whose name is f and whose input is x is multiplythevalueofhteinputxbythreeandaddtwotoit” or “The value of the output of the function f for input x is the value of 3x + 2”.

y = f(x) This means “The value of the output of the function f for input x is to be given the name y”. These are NOT equations and they are NOT identities. ————————————- The whole current mess arises from the use of the equals sign for “gives” or “makes”, or “we get”, as in “3 + 5 makes 8”, or “If we multiply 4 by 6 we get 24”, and we write

3 + 5 = 8, and 4 x 6 = 24 3 + 5 is 8 and 4 x 6 is 24 would be better.

The newfangled term “number sentence” appears to have been invented in order to avoid dealing with the correct mathematical jargon, but I see it as making things EVEN worse,